In your wave lab in Harvard Universities, congratulations on the scholarship, suppose you designed an oscillator in such a way that its motion is restricted along the y axis where the force on the system with mass m you designed it to be proportional to cubic xa) deduce the potential energy function for the oscilator, PE at x=0b) the time required for thr body to move from quilibruim at x=0 to an amplitude A is 1/4 of a periodic time of the motion. deduce this duration and periodic timec) based on calculations of part(b), does the periodic time depend on the amplitude a of oscillation? does your design produce simple harmonic motion ?